Current ball-and-socket connections are often permanent connections which do not permit removal of the ball from the socket or the use of different balls with the same socket, resulting in increased equipment costs and limitations in customizability. Current ball-and-socket connections which do permit removal of the ball from the socket often require locking mechanisms which are difficult or time-consuming to operate, or do not permit a useful degree of rotation of the ball within the socket, or are not self-releasing. For example, current ball-and-hitch connections, such as those used to hitch a trailer to an automobile, often require a collar-like or pawl-like mechanism to move into place under the ball with the express goal of preventing easy release or self-release of the ball from the hitch.